In drilling wells for oil and gas exploration, understanding the structure and properties of the associated geological formation provides information to aid such exploration. Measurements in a borehole are typically performed to attain this understanding, where the measurements can include using acoustic signals. In processing of borehole acoustic signals, two main types of algorithms are employed: time-domain procedures and frequency-domain procedures. Time-domain procedures do not require a transformation and they are computationally efficient. Time-domain procedures also allow application of fans based on arrival times of signals. Fans are filters that can operate on data based on a model of what data should and what data should not appear. Fans can be used to reject noise and acquire data. Fans can be particularly useful to eliminate unwanted modes.
However, time-domain procedures suffer from interference of different frequencies, which may constructively or destructively interact. Furthermore, time-domain procedures are mostly influenced by the dominant frequency of the signal, which may produce slownesses that are higher or lower than the actual formation slowness due to dispersive behavior of signals. Slowness, which is proportional to the inverse of velocity, is the amount of time for a wave to travel a certain distance. Even though manual application of digital filters partially solves this problem, such application may be a tedious process that requires manual work by an experienced log analyst. Frequency-domain procedures, on the other hand, can produce dispersion curves, which can be directly interpreted to recover the actual formation slowness. Frequency-domain procedures do not operate with time-based information, such as the time-slowness fans based on arrival times. Partly because an easy method to clean the signal is not available with frequency processing, frequency-domain procedures are usually only utilized for quality control. Further, the usefulness of such traditional measurements may be related to the precision or quality of the information derived from such measurements.